Question

Find Laplace transform L\left\{10e^{-5t}\sin\frac{t}{2}\right\}

Laplace transform
ANSWERED
asked 2021-09-15

Find Laplace transform \(L\left\{10e^{-5t}\sin\frac{t}{2}\right\}\)

Expert Answers (1)

2021-09-16

Solution:
\(KL\left\{10e^{-5t}\sin\left(\frac{t}{2}\right)\right\}\)
\(=10L\left\{e^{-5t}\sin\left(\frac{t}{2}\right)\right\}\)
as we know that
\(\displaystyle{e}^{{-{5}{t}}}{\sin{{\left({\frac{{{t}}}{{{2}}}}\right)}}}\rightarrow{\frac{{{2}}}{{{4}{\left({s}+{5}\right)}^{{2}}+{1}}}}\)
\(\therefore L\left\{10e^{-5t}\sin\left(\frac{t}{2}\right)\right\} \rightarrow \frac{20}{4(s+5)^2+1}\)

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